Impact of time-dependent earthquake recurrence modelling on probabilistic seismic hazard analysis

The (re)insurance industry has traditionally used a memoryless, time-independent (i.e., Poissonian) model for representing earthquake recurrence in seismic loss (risk) calculations. However, time-dependent renewal models, which account for the time elapsed since the last event, are more appropriate for modelling the longterm characteristics of cyclical mainshock occurrences in fault-based seismic hazard assessments. This study first reviews the main features and advantages of some of the most used time-dependent models for mainshock recurrence, and provides a critical discussion on their calibration and possible combination. A simple casestudy fault is used to quantify the changes in seismic hazard estimates resulting from the use of time-dependent Brownian Passage-Time (BPT) models instead of the conventional Poisson process. The considered fault is the Ohariu Fault in New Zealand, which is one of the major sources of earthquake hazard for the city of Wellington. BPT model parameters are calibrated using the maximum likelihood estimation (MLE) method together with paleoseismic data published in the literature. Results from this study show that the use of a timedependent BPT model can lead to a significant over- or under-estimation of the seismic hazard compared to the time-independent Poisson model, depending on the ratio between the time elapsed since the last event and the mean recurrence time of the fault. The simple single-fault case study also highlights the potential need for a combination of time-dependent models in actual earthquake risk models, since the single BPT model produces unrealistically low seismic hazard estimates for time periods in the immediate aftermath of an earthquake occurrence